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If x^ydoty^x=1,p rov et h a t(dy)/(dx)=-...

If `x^ydoty^x=1,p rov et h a t(dy)/(dx)=-(y(y+xlogy)/(x(ylogx+x)`

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Given,`x^y=y^x`
`logx^y=logy^x`
`ylogx=xlogy`
Differentiating
`(dy/dx)​logx+y/x​=logy+(x​dy)/(ydx)`
​ =`(dy/dx)(logx−x/y​)=logy−y/x`
​ ...
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RD SHARMA-DIFFERENTIATION-Solved Examples And Exercises
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  2. Differentiate the following function tan2x

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  3. If x^ydoty^x=1,p rov et h a t(dy)/(dx)=-(y(y+xlogy)/(x(ylogx+x)

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  12. Differentiate the following function with respect to x : sin^(-1...

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  13. Differentiate the following function with respect to x : tan^(-1...

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